Non-monotonic variation of the exchange energy in double elliptic quantum dots

We study the properties of a few-electron system confined in coupled elongated quantum dots (QDs) using a model Gaussian potential and the numerical exact diagonalization technique. In the absence of magnetic fields, as the aspect ratio r between the QD extensions in the directions perpendicular and parallel to the coupling directions increases, the exchange energy exhibits a sharp variation at the specific value r = 3.9, before (after) which the exchange energy increases (declines). The sharp variation occurs because of a sudden change in the single-particle configuration of the triplet state. The stability region with one electron in each of the QDs is found to shrink, and finally vanishes as it becomes progressively easier to localize both electrons into the QD with the lower electron potential energy. For r>3.9, the first singlet-triplet transition shifts to a small magnetic field.